Structured P2P systems based on distributed hash tables are a popular choice for building large-scaled data management systems. Generally, they only support exact match queries, but data heterogeneities often demand for more complex query types, particularly similarity queries. In this work, we suggest a vertical data organization, which allows for efficient processing of similarity queries on instance as well as on schema level, and we introduce corresponding physical similarity operators. Our novel approach is shown to be suitable in conjunction with P-Grid, as an example of robust, large-scaled and self-organizing P2P systems.